As far as I know, the Xbox One and PS4 started the trend of reading nothing from the disc after install. The disc just acts as instalation media and a physical authenticator.

I feel like something odd is going on. Are you exploring much and capturing wild pokemon? I haven’t played the latest gen but Let’s Go, Shield, and Legends Arceus were all very difficult to not get over leveled in most of the time. I tend to spend a lot of time running around and trying to get at least one of every species that I come across. The team wide experience can really get you over leveled fast unless you are rotating mons on your team frequently.

Don’t think this is exactly what you’re asking, but among actual old games, A Link to the Past and Super Metroid are both highly playable and highly replayable pixel graphics games.